The paper investigates the effect of variations in soil type, rainfall, N fertilizer amount and crop prices on the objectives of arable farms operating in Nitrogen Vulnerable Zones (NVZs) and receiving the Single Farm Payment (SFP). Sensitivity analysis was carried out using a mixed-integer programming (MIP) arable farm model (farmR). The farmR model estimates the arable farming objectives of interest: farm profit, crop complexity and risk minimization. Applying the 2014 SFP flat rate and the maximum N limits (N max) values (prescribed in the NVZ guidelines) to each crop, N max was varied under different soil types and rainfall interactions. Crop prices were also varied to illustrate the effectiveness of the SFP under a scenario of high crop prices. The results showed that even though applying N above N max increases farm productivity under all soil and rainfall interactions, doing so and forgoing the SFP reduces farm productivity and increases risk. The SFP thus acts as a payment for the opportunity cost to farms for not being able to apply N above N max. However under a scenario of crop price increases, applying above N max and forfeiting the SFP could generate higher productivity than at the N max level.